Ok, the line will cut the y axis where x=0.
Substitute x=0 into the equation, and you get y=-2. So point of interception is at:
(0,-2)
Now, the line will cut the x axis where y=0. To find this, we can try to factorise:

-4x^2-9x-2=0
4x^2+9x+2=0
(4x+1)(x+2)=0
x=-2 and x=-1/4
x intercepts are and

Parabolas are symmetrical, so if you take the x intercepts, the line of symmetry will be halfway between them. (wow, nasty numbers)
x=-1.125 is the line of symmetry.

A question about the vertex: Have you covered differentiation?

Also, how would I graph this as a parabola? If both x are on the negative side